In a wireless communication system, a radio signal propagates from a transmitter to a receiver. The time delay of the received signal corresponds to the length of the specific propagation path. Delay estimation has long been recognized as an important topic in wireless communications, and is closely related to other important issues such as channel estimation and ranging. Specifically, in the recent fast-developing UWB (ultra-wide band) technologies, delay estimation has been acknowledged as a main approach to ranging with high precision.
For simplicity, consider a signal propagates via a single path from a transmitter to a receiver. The received signal consists of the transmit signal with a certain time delay and additive noise. In the continuous time domain, a typical delay estimation method is to detect the time instant corresponding to the peak of a correlation function obtained by correlating the received signal and a template waveform equivalent to the transmit signal. In practice, digital (uniform) sampling is an indispensable operation in a wireless system. In this invention, digital sampling on the correlation function is assumed. Hence, the continuous function is converted into multiple discrete samples. The simplest delay estimation method based on these samples is to find the time instant associated with the largest sample, which is referred to as the direct-pick method herein. This method has the advantage of simplicity, yet has a main limitation that the estimation error can be very large with a low sampling frequency. In order to improve the estimation accuracy, interpolation and digital filtering techniques are adopted in delay estimation, where sample data are further processed. For example, in [1] ([1] E. F. Gueuning, M. Varlan, E. C. Eugene and P. Dupuis, “Accurate distance measurement by an autonomous ultrasonic system combining time-of-flight and phase-shift methods,” IEEE Trans. Instrumentation and Measurement, vol. 46, no. 6, pp. 1236-40, December 1997.), a digital lowpass filter is implemented to remove unwanted spectral signal components caused by sampling. These schemes, however, do not take into account such important information as the pre-knowledge of the autocorrelation function of the transmit signal and statistical characteristics of noise components in the sample data.